E7.13 A unity feedback system has a loop transfer function

L(s) = G(s)G(s) = (s+4) s(s+2)(s+ z) (a) Draw the root locus as z varies from 0 to 100. (b) Using the root locus, estimate the percent over- shoot and settling time (with a 2% criterion) of the sys- tem at z = 1, 2, and 3 for a step input. (c) Determine the actual overshoot and settling time at z = 1, 2, and 3.